.TH DPPCON 1 "November 2006" " LAPACK routine (version 3.1) " " LAPACK routine (version 3.1) " .SH NAME DPPCON - the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite packed matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by DPPTRF .SH SYNOPSIS .TP 19 SUBROUTINE DPPCON( UPLO, N, AP, ANORM, RCOND, WORK, IWORK, INFO ) .TP 19 .ti +4 CHARACTER UPLO .TP 19 .ti +4 INTEGER INFO, N .TP 19 .ti +4 DOUBLE PRECISION ANORM, RCOND .TP 19 .ti +4 INTEGER IWORK( * ) .TP 19 .ti +4 DOUBLE PRECISION AP( * ), WORK( * ) .SH PURPOSE DPPCON estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite packed matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by DPPTRF. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). .SH ARGUMENTS .TP 8 UPLO (input) CHARACTER*1 = \(aqU\(aq: Upper triangle of A is stored; .br = \(aqL\(aq: Lower triangle of A is stored. .TP 8 N (input) INTEGER The order of the matrix A. N >= 0. .TP 8 AP (input) DOUBLE PRECISION array, dimension (N*(N+1)/2) The triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T, packed columnwise in a linear array. The j-th column of U or L is stored in the array AP as follows: if UPLO = \(aqU\(aq, AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j; if UPLO = \(aqL\(aq, AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n. .TP 8 ANORM (input) DOUBLE PRECISION The 1-norm (or infinity-norm) of the symmetric matrix A. .TP 8 RCOND (output) DOUBLE PRECISION The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an estimate of the 1-norm of inv(A) computed in this routine. .TP 8 WORK (workspace) DOUBLE PRECISION array, dimension (3*N) .TP 8 IWORK (workspace) INTEGER array, dimension (N) .TP 8 INFO (output) INTEGER = 0: successful exit .br < 0: if INFO = -i, the i-th argument had an illegal value